Degeneracy measures for the algebraic classification of numerical spacetimes - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: We study the issue of algebraic classification of the Weyl curvature tensor,with a particular focus on numerical relativity simulations. The spacetimes ofinterest in this context, binary black hole mergers, and the ringdowns thatfollow them, present subtleties in that they are generically, strictlyspeaking, Type I, but in many regions approximately, in some sense, Type D. Toprovide meaning to any claims of -approximate- Petrov class, one must define ameasure of degeneracy on the space of null rays at a point. We will investigatesuch a measure, used recently to argue that certain binary black hole mergersimulations ring down to the Kerr geometry, after hanging up for some time inPetrov Type II. In particular, we argue that this hangup in Petrov Type II isan artefact of the particular measure being used, and that a geometricallybetter-motivated measure shows a black hole merger produced by our groupsettling directly to Petrov Type D.



Author: Robert Owen

Source: https://arxiv.org/







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